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John, the lighthouse keeper, is worried because his light isn't going far enough for boats to see. He needs to figure out what angle the light needs goes out in order for boats to see it. The lighthouse is 225 ft tall and he is told that the light needs to stretch out to 1000 ft.

1000 ft.﻿

﻿X ﻿

225 ft.﻿

John uses the inverse of cosine to find the angle. he sets the problem up as Tan-1(225/1,000) and gets 13 deg

1000 ft.﻿

13 deg﻿ ﻿

225 ft.﻿

So, when John adjusts the light to 13 deg he realizes that the light only stretches 52 ft.

52 ft.﻿

13 deg﻿ ﻿

225 ft.﻿

So, John, realizing that he messed up, goes to look for what he did wrong. turns out when using Tan he did adjacent/opposite and it gave him the wrong angle

X﻿

52 ft.﻿

X﻿

13 deg﻿ ﻿

225 ft.﻿

Now that John knows that he mixed up Tangent, he sets the problem up correctly. this time he does Tan-1(1,000/225) and gets 77o﻿. So John sets the light to 77o and now boats will be able to see the light and get to shore safely